Internal problem ID [627]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+13 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
dsolve(diff(y(x),x$2) +6*diff(y(x),x)+13*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-3 x} \sin \left (2 x \right )+c_{2} {\mathrm e}^{-3 x} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 26
DSolve[y''[x]+6*y'[x]+13*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \\ \end{align*}